No, we can't become the party of censorship. Look, the dominant narrative is that the Republicans are the "morality" party and we're not. If you want to overturn that narrative in certain ways, it'll take years to do it. Right now, when Republicans start concerning themselves with these things, whether they make any legislatives moves or not, it's because they're worried about "values." If Democrats do it it'll be because we're a bunch of prudish scolds who want to take away your porn.
The Dems should be going after the techno-lib vote by fighting against the Intellectual Property grab which is currently going on. Give people their porn, their Napster, and their unfettered Tivo. And, yes, I am respectful of genuine intellectual property rights but DMCA, the Mickey Mouse Preservation Act copyright extension and the inevitable progeny of both will soon make it impossible to say or do anything without handing over a license fee.